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2017 | OriginalPaper | Chapter

Robust Clustering Algorithms Employing Fuzzy-Possibilistic Product Partition

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Abstract

One of the main challenges in the field of clustering is creating algorithms that are both accurate and robust. The fuzzy-possibilistic product partition c-means clustering algorithm was introduced with the main goal of producing accurate partitions in the presence of outlier data. This chapter presents several clustering algorithms based on the fuzzy-possibilistic product partition, specialized for the detection of clusters having various shapes including spherical and ellipsoidal shells. The advantages of applying the fuzzy-possibilistic product partition are presented in comparison with previous c-means clustering models. Besides being more robust and accurate than previous probabilistic-possibilistic mixture partitions, the product partition is easier to handle due to its reduced number of parameters.

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Literature
1.
go back to reference Bezdek, J. C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981) Bezdek, J. C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)
2.
go back to reference Davé, R. N.: Characterization and detection of noise in clustering. Patt. Recogn. Lett. 12, 657–664 (1991) Davé, R. N.: Characterization and detection of noise in clustering. Patt. Recogn. Lett. 12, 657–664 (1991)
3.
go back to reference Menard, M., Damko, C., Loonis, P.: The fuzzy \(c+2\) means: solving the ambiguity rejection in clustering. Patt. Recogn. 33, 1219–1237 (2000) Menard, M., Damko, C., Loonis, P.: The fuzzy \(c+2\) means: solving the ambiguity rejection in clustering. Patt. Recogn. 33, 1219–1237 (2000)
4.
go back to reference Chintalapudi, K. K., Kam, M.: A noise-resistant fuzzy \(c\)-means algorithm for clustering. IEEE World Congr. Comput. Intell. 1458–1463 (1998) Chintalapudi, K. K., Kam, M.: A noise-resistant fuzzy \(c\)-means algorithm for clustering. IEEE World Congr. Comput. Intell. 1458–1463 (1998)
5.
go back to reference Alanzado, A. C., Miyamoto, S.: Fuzzy \(c\)-means clustering in the presence of noise cluster for time series analysis. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 3558, 156–163 (2005) Alanzado, A. C., Miyamoto, S.: Fuzzy \(c\)-means clustering in the presence of noise cluster for time series analysis. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 3558, 156–163 (2005)
6.
go back to reference Krishnapuram, R., Keller, J. M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993) Krishnapuram, R., Keller, J. M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993)
7.
go back to reference Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996) Barni, M., Capellini, V., Mecocci, A.: Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4, 393–396 (1996)
8.
go back to reference Timm, H., Borgelt, C., Döring, C., Kruse, R.: An extension to possibilistic fuzzy cluster analysis. Fuzzy Sets and Systems 147, 3–16 (2004) Timm, H., Borgelt, C., Döring, C., Kruse, R.: An extension to possibilistic fuzzy cluster analysis. Fuzzy Sets and Systems 147, 3–16 (2004)
9.
go back to reference Pal, N. R., Pal, K., Bezdek, J. C.: A mixed \(c\)-means clustering model. Proc. IEEE Int’l Conf. Fuzzy Systems (FUZZ-IEEE), pp. 11–21 (1997) Pal, N. R., Pal, K., Bezdek, J. C.: A mixed \(c\)-means clustering model. Proc. IEEE Int’l Conf. Fuzzy Systems (FUZZ-IEEE), pp. 11–21 (1997)
10.
go back to reference Pal, N. R., Pal, K., Keller, J. M., Bezdek, J. C.: A possibilistic fuzzy \(c\)-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13, 517–530 (2005) Pal, N. R., Pal, K., Keller, J. M., Bezdek, J. C.: A possibilistic fuzzy \(c\)-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13, 517–530 (2005)
11.
go back to reference Szilágyi, L.: Fuzzy-Possibilistic Product Partition: a novel robust approach to c-means clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 6820, 150–161 (2011) Szilágyi, L.: Fuzzy-Possibilistic Product Partition: a novel robust approach to c-means clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 6820, 150–161 (2011)
12.
go back to reference Gunderson, R.: An adaptive FCV clustering algorithm. Int. J. Man-Mach. Stud. 19, 97–104 (1983) Gunderson, R.: An adaptive FCV clustering algorithm. Int. J. Man-Mach. Stud. 19, 97–104 (1983)
13.
go back to reference Krishnapuram, R., Nasraoui, O., Frigui, H.: A fuzzy \(c\) spherical shells algorithm: a new approach. IEEE Trans. Neur. Netw. 3, 663–671 (1992) Krishnapuram, R., Nasraoui, O., Frigui, H.: A fuzzy \(c\) spherical shells algorithm: a new approach. IEEE Trans. Neur. Netw. 3, 663–671 (1992)
14.
go back to reference Davé, R. N.: Generalized fuzzy \(c\)-shells clustering and detection of circular and elliptical boundaries. Pattern Recogn. 25(7), 713–721 (1992) Davé, R. N.: Generalized fuzzy \(c\)-shells clustering and detection of circular and elliptical boundaries. Pattern Recogn. 25(7), 713–721 (1992)
15.
go back to reference Frigui, H., Krishnapuram, R.: A comparison of fuzzy shell clustering methods for the detection of ellipses. IEEE Trans. Fuzzy Syst. 4, 193–199 (1996) Frigui, H., Krishnapuram, R.: A comparison of fuzzy shell clustering methods for the detection of ellipses. IEEE Trans. Fuzzy Syst. 4, 193–199 (1996)
16.
go back to reference Krishnapuram, R., Frigui, H., Nasraoui, O.: New fuzzy shell clustering algorithms for boundary detection and pattern recognition. SPIE Proc. Robot. Comp. Vis. 1607, 1460–1465 (1991) Krishnapuram, R., Frigui, H., Nasraoui, O.: New fuzzy shell clustering algorithms for boundary detection and pattern recognition. SPIE Proc. Robot. Comp. Vis. 1607, 1460–1465 (1991)
17.
go back to reference Davé, R. N., Bhaswan, K.: Adaptive fuzzy \(c\)-shells clustering and detection of ellipses. IEEE Trans. Neural Netw. 3(5), 643–662 (1992) Davé, R. N., Bhaswan, K.: Adaptive fuzzy \(c\)-shells clustering and detection of ellipses. IEEE Trans. Neural Netw. 3(5), 643–662 (1992)
18.
go back to reference Krishnapuram, R., Frigui, H., Nasraoui, O.: Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation - Part I. IEEE Trans. Fuzzy Syst. 3, 29–43 (1995) Krishnapuram, R., Frigui, H., Nasraoui, O.: Fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation - Part I. IEEE Trans. Fuzzy Syst. 3, 29–43 (1995)
19.
go back to reference Bezdek, J.C., Hathaway, R.J., Pal, N.R.: Norm induced shell prototype (NISP) clustering. Neur. Parall. Sci. Comput. 3, 431–450 (1995) Bezdek, J.C., Hathaway, R.J., Pal, N.R.: Norm induced shell prototype (NISP) clustering. Neur. Parall. Sci. Comput. 3, 431–450 (1995)
20.
go back to reference Höppner, F.: Fuzzy shell clustering algorithms in image processing: fuzzy \(c\)-rectangular and 2-rectangular shells. IEEE Trans. Fuzzy Syst. 5, 599–613 (1997) Höppner, F.: Fuzzy shell clustering algorithms in image processing: fuzzy \(c\)-rectangular and 2-rectangular shells. IEEE Trans. Fuzzy Syst. 5, 599–613 (1997)
21.
go back to reference Steinhaus, H.: Sur la division des corp materiels en parties. Bull. Acad. Pol. Sci. C1 III. (IV) 801–804 (1956) Steinhaus, H.: Sur la division des corp materiels en parties. Bull. Acad. Pol. Sci. C1 III. (IV) 801–804 (1956)
22.
go back to reference Szilágyi, L., Szilágyi, S. M., Benyó, B., Benyó, Z.: Intensity inhomogeneity compensation and segmentation of MR brain images using hybrid \(c\)-means clustering models. Biomed. Sign. Proc. Contr. 6, 3–12 (2011) Szilágyi, L., Szilágyi, S. M., Benyó, B., Benyó, Z.: Intensity inhomogeneity compensation and segmentation of MR brain images using hybrid \(c\)-means clustering models. Biomed. Sign. Proc. Contr. 6, 3–12 (2011)
23.
go back to reference Szilágyi, L.: Robust spherical shell clustering using fuzzy-possibilistic product partition. Int. J. Intell. Syst. 28, 524–539 (2013) Szilágyi, L.: Robust spherical shell clustering using fuzzy-possibilistic product partition. Int. J. Intell. Syst. 28, 524–539 (2013)
24.
go back to reference Szilágyi, L., Varga, Zs. R., Szilágyi, S. M.: Application of the fuzzy-possibilistic product partition in elliptic shell clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 8825, 158–169 (2014) Szilágyi, L., Varga, Zs. R., Szilágyi, S. M.: Application of the fuzzy-possibilistic product partition in elliptic shell clustering. Proc. Modeling Decisions in Artificial Intelligence (MDAI), Lect. Notes Comp. Sci. 8825, 158–169 (2014)
25.
go back to reference Anderson, E.: The IRISes of the Gaspe peninsula. Bull. Amer. IRIS Soc. 59, 2–5 (1935) Anderson, E.: The IRISes of the Gaspe peninsula. Bull. Amer. IRIS Soc. 59, 2–5 (1935)
26.
go back to reference Gosztolya, G., Szilágyi, L.: Application of fuzzy and possibilistic \(c\)-means clustering models in blind speaker clustering. Acta Polytech. Hung. 12(7), 41–56 (2015) Gosztolya, G., Szilágyi, L.: Application of fuzzy and possibilistic \(c\)-means clustering models in blind speaker clustering. Acta Polytech. Hung. 12(7), 41–56 (2015)
Metadata
Title
Robust Clustering Algorithms Employing Fuzzy-Possibilistic Product Partition
Author
László Szilágyi
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-47557-8_7

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